Photoelectric Cross Sections Research Articles

Solid geometrv based modelling of non-uniform attenuation and compton scattering in objects for SPECT imaging systems

A solid geometry based approach is used to model non-uniform attenuation and Compton scattering in irregularly shaped objects for Monte Carlo simulated single photon emission computed tomography (SPECT) imaging systems. The shape of an object is described by a combination of object primitives: ellipsoids, elliptical cylinders, tapered elliptical cylinders, rectangular solids, and their halves, quarters, and eighths, based on set union, intersection, and difference. The primitives are then assigned density and energy-dependent photoelectric and Compton cross sections. This approach is validated in two steps. Firstly, only non-uniform attenuation is included. The transaxial images of a simulated thorax phantom are reconstructed using a modified Chang's technique for nonuniform attenuation. Secondly, detected Compton scattering is added to the model. Scatter fraction of a point source in a water cylinder is used to validate our scatter model for uniform scattering media. The difference between simulated and experimental results is on the order of 10%. For the model of nonuniform attenuation and detected Compton scattering, a thorax phantom is used for validation. Normalized profiles across the center of the sphere projections for simulation and experiment are observed to have insignificant difference. These results validate our object modelling approach for nonuniform attenuation and Compton scattering. The performance of the solid model is demonstrated to be faster and require substantially less parameter storage than a voxel based model.

An interesting application of scaling procedure to x-ray spectrometry

An analytical approximation for the simple description of the photoelectric cross-section as a function of the photon energy and atomic number is obtained using a scaling procedure.

Direct measurement of total and photoelectric cross sections of medium and high Z elements in the range 48 ⩽ Z ⩽ 83 present in compounds for 123.6 keV photons

A new, simple and direct method proposed earlier by us for the measurement of total photoelectric cross sections of elements at 123.6 keV has been extended here to obtain fairly accurate total photoelectric cross sections of medium and heavy elements present in various compounds by measuring their K x-ray fluorescence intensities induced by 123.6 keV gamma rays using a NaI(Tl) spectrometer system attached to a 1 K MCA in a 2 π geometrical configuration. The compounds of various elements in the region 48 ⩽ Z ⩽ 83 have been employed in the form of circular pellets for measurements. The K x-ray fluorescence cross section σ K is determined by measuring the K x-ray fluorescence intensity, from which the total photoelectric cross section τ is obtained by using the theoretical value of K fluorescence yield of the element. From the measured total photoelectric cross section, the K-shell photoelectric cross section is evaluated. A 50–20% transmission region in the broad beam geometry configuration is identified for measuring reasonably accurate total mass attenuation coefficients for the incident and for the K x-ray radiations in the same target. The values agree fairly well with the corresponding mass attenuation coefficients obtained using a stringent narrow beam geometry configuration. The total mass attenuation coefficients μ i and μ e of high Z elements were derived from the measured attenuation coefficients μ i and μ e of compounds using the mixture-rule for the incident and for the K x-ray energies by assuming μ i and μ e values of low Z elements present in the compounds. All these parameters are compared with their corresponding theoretical values and good agreement between them is obtained.

Improvements in computation of form factors

Tables for form factors and anomalous dispersion are of wide general use in the UV, X-ray and γ-ray communities,and have existed for a considerable period of time. The generality of these works has entailed numerous simplications compared to detailed relativistic S-matrix calculations. However, the latter calculations do not appear to give convenient tabular application for the range of Z and energy of general interest, whereas the former tables have large regions of limited validity throughout the range of Z and energies, and in particular have limitations with regard to extrapolition to energies outside tabulated ranges. Intermediate theoretical and procedural assumptions limit the precision and applicability of available tabulations and procedures. This paper identifies regions of Z and energy where these assumptions fail and the improvement which can be achieved by their avoidance, both in tabulated ranges and by extrapolation. Particular concern involves the application of the dispersion relation to derive Re(f;) from photoelectric absorption cross-sections. Revised formulae can lead to significant qualitative and quantitative improvement, particularly above 30–60 keV energies, near absorption edges, or at 30–3000 eV energies. Current experimental syntheses are not superceded by this approach, but examples are given where predictions underlying revised theoretical tables are in qualitative agreement with experiment as opposed to results in available syntheses. Recent theoretical developments involving small corrections to earlier form factors are of limited usefulness if the relatively large corrections discussed herein are not included.

Photoelectric absorption cross sections with variable abundances

Polynomial fit coefficients have been obtained for the energy dependences of the photoelectric absorption cross sections of 17 astrophysically important elements. These results allow the calculation of X-ray absorption in the energy range 0.03-10 keV in material with noncosmic abundances.

X-ray attenuation coefficients and photoelectric cross sections of Cu and Fe in the range 3 keV to 29 keV

A new X-ray source has been obtained by proton excitation of elemental or compound targets. Using this X-ray source and Si(Li) detector system the mass attenuation coefficients have been determined for copper in the energy range 3.3–29.1 keV, for iron in 3.3–20 keV. The experimental uncertainties of the attenuation coefficients have been reduced to ±1% for intense isolated characteristic X-rays. The total photoelectric cross sections have been obtained by subtracting scattering cross sections from the measured total cross sections. The comparisons of the present experimental results with the past values, as well as between the experimental values and the theoretical calculations, have been presented and discussed.

A comparison of experimental and theoretically derived sensitivity factors for XPS

AbstractX‐ray photoelectron spectroscopy sensitivity factors for elements from lithium to zinc have been determined experimentally using standard compounds. These are found to differ quite considerably from those theoretically calculated using Scofield's photoelectric cross‐sections, but are in good agreement with other experimentally derived databases in the literature. It is concluded that Scofield's cross‐sections are in error and that a correction factor must be employed if they are to be used for the calculation of XPS sensitivity factors.

Mass attenuation coefficients for elements measured with characteristic x-rays from targets excited by energetic proton

The characteristic x-rays from elemental or compound targets excited by energetic proton are quasi-monochromatic x-ray sources. The advantages of high line/background ratio, controllable intensity as well as many available energies, make them suitable for applications in many important fields. The total mass attenuation cross sections of yttrium have been systematically measured by using this kind of x-ray source. The accuracy of experimental data has been improved to ± 1%, which is much better than that of earlier results. The contributions of the coherent and incoherent scattering cross sections have been calculated in accordance with the present experimental condition. And the total photoelectric cross sections have been obtained by subtracting the scattering cross section from the measured total cross sections. The comparisons of our experimental results with the available data of earlier investigations as well as with the theoretical calculations have been presented and discussed.

Measurements of mass attenuation coefficients of yttrium with characteristic lines from elements excited by energetic protons

The characteristic X-rays from elemental or compound targets excited by a proton beam of tandem accelerator is a quasimonochromatic X-ray source. The mass attenuation coefficients of yttrium have been systematically measured in the region 3.3 keV to 29.1 keV by using this kind of X-ray source. The experimental uncertainties of mass attenuation coefficients have been reduced to ±1%. The coherent scattering cross sections have been calculated in accordance with the present experimental condition. The total photoelectric cross sections have been obtained by subtracting scattering cross section from the measured total cross sections.

Z-dependence of photoelectric cross-section in the energy region of absorption edges (6.4÷136.47) keV

Total photon cross-sections are measured by the transmission method using a Si(Li) spectrometer on a good geometry set-up in elements 6⩽Z⩽92 at eight energies in the region of absorption edges. Photoelectric cross-sections are deduced from these by subtracting the theoretical contributions due to coherent and incoherent scattering. These values along with previous experimental data are used to study theZ-dependence of photoelectric cross-section in the energy region of absorption edges. TheZ-exponent is found to vary from 3.6 to 4.6 in general agreement with those evaluated using Scofield’s theoretical photoelectric cross-sections.

The use of mössbauer scattering spectroscopy for the determination of physical parameters

The procedures for the determination of the linewidth of the scatterer, the surface density of the scattering layer, the angular correlation function, the interference parameter, the Debye-Waller factor for Rayleigh scattering, Lamb-Mossbauer factors for the absorption and reemission of Mossbauer radiation, the mass resonance absorption coefficient of Mossbauer radiation, and attenuation coefficients for Rayleight and Compton scattering are considered. It is shown that for the conversion of experimentally determined reduced attenuation coefficients of different absorption or scattering processes to the cross sections or mass attenuation coefficients, one needs to know the photoelectric absorption cross section or mass photoelectric absorption coefficient of Mossbauer radiation in the K-shell of Fe, which can be determined experimentally.

L-shell X-ray opacity of many-electron atoms

The study presents a formulation for obtaining the L-shell photoelectric cross section (sigma sub L) for many-electron atomic systems. A scaling law is suggested for the evaluation of the contribution to sigma sub L from 2s and 2p ejection from a general system in any ionization state. The formula is expressed in terms of the effective nuclear charge (Z sub 2s and Z sub 2p) seen by the corresponding bound electrons, with Z sub 2s and Z sub 2p, obtained from improved screening constants derived in a recent investigation. A comparison is made of Hartree-Fock and hydrogenic expressions for sigma sub L with experimental results for atomic neon at X-ray photon energies, providing the basis for the scaling law and an approximate energy dependence for the cross sections. The special case of sigma sub L for atomic Fe is considered in detail. This L edge has structure because of the different threshold for 2s and 2p photoejection; the latter has fine structure.

A new direct method to determine total atomic photoelectric cross sections at 123.6 keV

A new, simple and direct method has been proposed to obtain fairly accurate total atomic photoelectric cross sections by measuring the K x-ray fluorescence spectrum induced by 123.6 keV gamma rays for elements in the region 42 ⩽ Z ⩽ 82 by employing a NaI(Tl) spectrometer system in a 2 π geometry set up. In a single run the K x-ray emission cross section, the total mass attenuation coefficient of the exciting radiation, the total mass attenuation coefficient of K x-rays in the same target and from them the total scattering cross section of the primary radiation have been determined. All the parameters are compared with their corresponding theoretical values and a good agreement between them is obtained.

Measurement of Ll, L alpha, L beta, and L gamma x-ray production cross sections in rare-earth elements by 60-keV photons.

Our earlier measurements [Shatindra, Allawadhi, and Sood, Phys. Rev. A 31, 2918 (1985)] of Ll, L\ensuremath{\alpha}, L\ensuremath{\beta}, and L\ensuremath{\gamma} x-ray production cross sections in elements with 73\ensuremath{\le}Z\ensuremath{\le}92 by 60-keV photons have been extended to 11 rare-earth elements in the range 57\ensuremath{\le}Z\ensuremath{\le}68 in order to examine enhancement in L-subshell x-ray production due to transfer of vacancies from the K to the L shell. The measured values of absolute cross sections have been interpreted in terms of K-shell photoelectric cross sections, probabilities of K\ensuremath{\rightarrow}L radiative and nonradiative transitions, L-subshell photoelectric cross sections, fluorescence yields, Coster-Kronig transition probabilities, and radiative decay rates. Fairly good agreement between the experimental and calculated values indicates indirectly the correctness of the theoretical calculations of the atomic parameters in terms of which the experimental results have been interpreted.

The energies and structure of X-ray K-absorption edges

Improved screening parameters are employed to compute the K threshold energies E(K) and photoelectric cross sections sigma(K) for the abundant atomic species of the interstellar gas. The E(K)-values for neutral C, N, and O differ from the values currently being employed in X-ray astronomy by several percent. The values are computed in an effective Coulomb field formulation, introducing an 'effective Coulomb' threshold, and convenient formulas are given for the extrapolation of the results to lower energies in the neighborhood of the real threshold energy. Within about 30-200 eV above threshold, the corrected cross sections display structure associated with direct secondary excitation of outer-shell electrons into the continuum. A unified description of this feature of the cross section is introduced, in terms of the secondary threshold energies and core relaxation factors. Both of these factors are computed with the improved screening parameters associated with the one-electron atomic states of the many-electron systems.

Quantum theory of the Borrmann effect.

In the phenomenon of diffraction of an electromagnetic wave in a lattice, the phase relations between the transmitted wave and the diffracted wave are fundamental. A vector can be written that describes the quantum state of the radiation in the above-mentioned case, and the photoelectric absorption cross section can be computed. It will be proved that the way the dynamical theory of x-ray diffraction deals with absorption is not correct because it does not consider the interference between the \ensuremath{\alpha} and \ensuremath{\beta} rays; this phenomenon causes the failure of the dynamical theory in the explication of the Borrmann effect, which will be explained by means of a theory proposed herein. In addition, a new phenomenon is described that is not expected by the dynamical theory, the coherent scattering of photons from the \ensuremath{\beta} ray to the \ensuremath{\alpha} ray; such a phenomenon is the real origin of the \ensuremath{\beta}-ray extinction in the crystal and a quite anomalous expression for the extinction depth is found that is inversely proportional to the incident intensity.

Geochemical well logging in basalts: The Palisades Sill and the oceanic crust of Hole 504B

Geochemical well logging provides a continuous record of the variations in elemental abundances of the major rock‐forming oxides of Si, Al, Ca, Fe, Ti, and K, as well as S, Gd, U, Th, and the H and Cl in the formation and pore fluid. Through the additional measurement of the photoelectric capture cross section of the rock, the sum of Mg + Na can also be estimated. Though not as accurate as laboratory analyses of recovered core samples, the log‐derived abundances are precise enough to define the degree and extent of alteration, to identify igneous lithostratigraphy, and to calculate integrated chemical exchange between the oceanic crust and seawater. In this paper, the elemental yields from geochemical logging in basalts are calibrated against extensive XRF analyses of cutting samples from the Lamont 2 test well into the diabases of the Palisades Sill, New York. Accuracy and precision of the log‐derived analyses are determined in the lower part of the well, and calibration equations are derived, which are then tested against core‐derived “standards” from the upper part of the well. The calibrated, log‐derived, elemental analyses are within one standard deviation of the core‐derived results (except for the Mg + Na curve, which is somewhat noisier). These calibrations are then applied to geochemical logs from the oceanic crustal basalts of Ocean Drilling Program hole 504B, where core recovery was less than 20% of the section. The accuracy and precision of the calibrated, log‐derived elemental abundances are tested against core‐derived standards from seven dike and sill intervals. Then the corrected elemental analyses are used to derive a mineralogy model for hole 504B that shows the oceanic crust to contain secondary mineralization in the form of celadonites and smectites in the pillow basalts and chlorites in the dikes that are largely confined to fracture and breccia zones. Cyclicity in the Al and other elemental logs was found to vary with the abundances of these alteration products and with eruption and intrusion event boundaries. The geochemical logging data are then used to estimate the integrated chemical exchange resulting from hydrothermal alteration of the oceanic crust that has occurred over the last 5.9 m.y. in hole 504B. The primary change is from Ca loss and Mg gain caused by the reaction of basalt with seawater. A large Si increase found in the transition zone between the pillows and dikes is attributed to precipitation of quartz during mixing of hot, up welling hydrothermal fluids and cold, downwelling seawater at what was once a major permeability discontinuity. The present low‐to‐high permeability transition in hole 504B is found 500 m shallower. The K budget requires significant addition to the uppermost pillow basalts both from high‐temperature depletion in the lower pillows and dikes and from low‐temperature exchange with seawater. The geochemical logs further document that the total chemical exchange between the oceanic crust and seawater is as important to the long‐term composition of the oceans as is the chemical input carried by rivers. Integrated “water/rock ratios” are then derived for the mass of seawater required to add enriched elements and the mass of hydrothermal fluid required to remove depleted elements in the oceanic crust of hole 504B. Whereas Ca, Mg, and K require relatively low water/rock ratios, high values for Si, Al, and Fe suggest that off‐axis, ridge‐flank exchange is as important to the total cation exchange budget as are ridge‐axis processes.

The Compton and photoelectric spectroscopy of multiply scattered photons

An analysis is made of the pulse height spectra of multiply scattered gamma -rays having energies between 0.01 and 0.7 MeV, whose interactions with matter are described by their Compton scattering and photoelectric absorption cross sections. It is shown that multiply scattered photon spectra generated in nonuniform media contain more than two significant spectral components. It is demonstrated that the variability of the spectra is due in part to the spatially nonuniform sampling of the medium by such devices. The most significant spectral components are displayed. A spectral sensitivity matrix that quantitatively relates the linear variations of the material properties to those of the spectra is defined. Analysis of this sensitivity matrix makes it possible to define a set of independent, characteristic spectroscopic components, each of which is uniquely related to a particular mode of cross section variation. The analysis is carried out for an ensemble of empirical data from a gamma - gamma device similar to those employed for borehole logging. >

Computer-Generated Corelike Descriptions from Open-Hole Logs (1)

A computer procedure extracts geological information from wireline logs and generates a well summary document similar to a core description. Lithology is determined by reference to a lithofacies database of responses from open-hole logs, comprising at least density, neutron, and gamma-ray logs, and preferably also sonic, photoelectric cross section, thorium, uranium, and potassium logs. Texture and structure are derived by analyzing dipmeter microresistivity curves. The various descriptive elements then are analyzed and combined using geological information encoded as rules or knowledge bases. The results of this technique provide a lithological zonation of the well showing bedding type (massive, laminated, etc.), parallelism of bed boundaries, presence and nature of heterogeneities, and sand/shale ratio. The geometry of sand/shale layers is defined with high precision. Resistivity trends and sedimentary dip distributions are displayed and provide elements for a sedimentological interpretation. The log-derived description must be calibrated with core data and can be extended to geologically similar uncored intervals. It can also serve to prepare and enhance the core description itself. Applications of this procedure to the appraisal of reservoir potential and the interpretation of borehole imagery illustrate how the method helps in understanding reservoir heterogeneity and shale distribution, which largely control fluid flow in the reservoir.

Type and distribution modes of clay minerals from well logging data

Typical shaly clastic reservoir rocks and/or shale intervals frequently contain varying amounts of different clay minerals. Most common clay minerals exhibit significant differences in their basic properties, including chemical composition, matrix density (g cc −1), photoelectric cross section ( Pe, barns per electron), hydrogen index ( HI), cation exchange capacity ( CEC, meq 100g −1), potassium (%), uranium (ppm), and thorium (ppm). These different properties and associated interpretive models allow the identification and quantitative evaluation of the major clay mineral groups such as smectite, illite, kaolinite, and chloride via geophysical well-log responses. Based on density, neutron, and natural gamma-ray spectral data, two important formation parameters, clay density ( P cl) and neutron response to 100% clay ( N cl), can be determined at every depth level over the computed interval of interest. No average clay property values from adjacent shale formations are required as input. Hence, the constraints inherent to other techniques, e.g. the assumption that clay properties in the clastic reservoir and adjacent shales are identical, do not apply. Having determined the two critical clay parameters, P cl and N cl, the clay volume ( V cl) is calculated simultaneously from both the potassium and thorium values. This V cl is essentially independent of the clay types. These three parameters ( p cl, N cl, V cl) then allow for the calculation of two important reservoir parameters at each depth level, namely, the cation exchange capacity ( CEC) and the hydrogen index ( HI). The resulting CEC and HI values then define the types of clay minerals present. On a CEC versus HI crossplot, the smectite (montmorillonite), illite and kaolinite/chlorite are grouped at three separate, clearly defined positions. Recently-developed interpretive refinements incorporate the photoelectric cross-section value, Pe, which also allows quantitative differentiation of kaolinite and chlorite. Hence, all four major clay mineral groups (smectite, allite, kaolinite, chlorite) can be evaluated via modern logging measurements. Field examples illustrate these concepts as applied to well completion, formation damage, and detailed clastic reservoir characteristics.